| Wavelet analysis absorbs the essence from real analysis, functional analysisand linear algebra theory, which is also the succession and development ofFourier analysis. The wavelet frames are one of the most important researchtopics in wavelet analysis. Because of the existence of the “redundant” functionwhich goes with wavelet tight frames, it makes that the process which wavelettight frames have various expression forms, so its numerical calculation is morestable.At present, most of the wavelet tight frames theories are based on2bands,although the calculation difficulty greatly reduces, but if it is necessary toanalysis the pulse or transient signal in the high frequency signal,2bandswavelet can not meet the demand, and increasing the number of bands is a kindof inevitable means to enhance the high-frequency signal processing effect. Now3bands,4bands wavelet tight frames have been researched. On the basis of these,with the help of multi-resolution analysis method and mainly using frame multi-resolution analysis, the construction method of binary6-bands wavelet tightframes is given, which can construct the corresponding wavelet tight frames ifany36order unitary matrix is given. Although its operation is more complex,this method can effectively deal with the pulse or transient signal in the highfrequency signal. Secondly, in the process of to restoring signal using wavelettight frames, for convenience of numerical calculation, the decomposition andreconstruction formulas of binary6-bands wavelet tight frames are offered.Because most signals in life are multi-dimensional, dynamic and its dataquantity also greatly grows, the requirements of storage device andcommunication channel are higher. Based on these, according to the properties ofconjugate filter, the construction method of2-dimensional wavelet orthogonal conjugate filter by the use of cosine function is designed, which lays thefoundation for further structuring scale function and wavelet function. |
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